Bayesian estimators in uncertain nested error regression models

JOURNAL OF MULTIVARIATE ANALYSIS

卷:153

Article

Sugasawa, Shonosuke¹  Kubokawa, Tatsuya² 

[1] Inst Stat Math, Risk Anal Res Ctr, 10-3 Midori Cho, Tachikawa, Tokyo 1908562, Japan

[2] Univ Tokyo, Fac Econ, Bunkyo Ku, 7-3-1 Hongo, Tokyo 1130033, Japan

关键词: Bayesian estimator;    Nested error regression model;    Posterior propriety;    Small area estimation;    Uncertain random effect;   

DOI  :  10.1016/j.jmva.2016.09.011

来源: Elsevier

【 摘 要 】

Nested error regression models are useful tools for the analysis of grouped data, especially in the context of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in each area is expressed as a mixture of a normal distribution and a positive mass at 0. For the estimation of the model parameters and prediction of the random effects, an objective Bayesian inference is proposed by setting non-informative prior distributions on the model parameters. Under mild sufficient conditions, it is shown that the posterior distribution is proper and the posterior variances are finite, confirming the validity of posterior inference. To generate samples from the posterior distribution, a Gibbs sampling method is provided with familiar forms for all the full conditional distributions. This paper also addresses the problem of predicting finite population means, and a sampling-based method is suggested to tackle this issue. Finally, the proposed model is compared with the conventional nested error regression model through simulation and empirical studies. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free